1 files changed, 197 insertions, 0 deletions
diff --git a/src/PJ_aitoff.cpp b/src/PJ_aitoff.cpp
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+/******************************************************************************
+ * Project:  PROJ.4
+ * Purpose:  Implementation of the aitoff (Aitoff) and wintri (Winkel Tripel)
+ *           projections.
+ * Author:   Gerald Evenden (1995)
+ *           Drazen Tutic, Lovro Gradiser (2015) - add inverse
+ *           Thomas Knudsen (2016) - revise/add regression tests
+ *
+ ******************************************************************************
+ * Copyright (c) 1995, Gerald Evenden
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ *****************************************************************************/
+
+#define PJ_LIB__
+
+#include <errno.h>
+#include <math.h>
+
+#include "proj.h"
+#include "projects.h"
+
+
+enum Mode {
+    AITOFF = 0,
+    WINKEL_TRIPEL = 1
+};
+
+struct pj_opaque {
+    double  cosphi1;
+    enum Mode mode;
+};
+
+
+PROJ_HEAD(aitoff, "Aitoff") "\n\tMisc Sph";
+PROJ_HEAD(wintri, "Winkel Tripel") "\n\tMisc Sph\n\tlat_1";
+
+
+
+#if 0
+FORWARD(s_forward); /* spheroid */
+#endif
+
+
+static XY s_forward (LP lp, PJ *P) {           /* Spheroidal, forward */
+    XY xy = {0.0,0.0};
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    double c, d;
+
+    if((d = acos(cos(lp.phi) * cos(c = 0.5 * lp.lam))) != 0.0) {/* basic Aitoff */
+        xy.x = 2. * d * cos(lp.phi) * sin(c) * (xy.y = 1. / sin(d));
+        xy.y *= d * sin(lp.phi);
+    } else
+        xy.x = xy.y = 0.;
+    if (Q->mode == WINKEL_TRIPEL) {
+        xy.x = (xy.x + lp.lam * Q->cosphi1) * 0.5;
+        xy.y = (xy.y + lp.phi) * 0.5;
+    }
+    return (xy);
+}
+
+/***********************************************************************************
+*
+* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
+*
+* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse
+* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
+* Third International Symposium Mathematical & Computational Applications,
+* pages 175{182, Turkey, September 2002.
+*
+* Expected accuracy is defined by EPSILON = 1e-12. Should be appropriate for
+* most applications of Aitoff and Winkel Tripel projections.
+*
+* Longitudes of 180W and 180E can be mixed in solution obtained.
+*
+* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
+*
+* Contact : dtutic@geof.hr
+* Date: 2015-02-16
+*
+************************************************************************************/
+
+static LP s_inverse (XY xy, PJ *P) {           /* Spheroidal, inverse */
+    LP lp = {0.0,0.0};
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    int iter, MAXITER = 10, round = 0, MAXROUND = 20;
+    double EPSILON = 1e-12, D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp, cp, cl, x, y;
+
+    if ((fabs(xy.x) < EPSILON) && (fabs(xy.y) < EPSILON )) { lp.phi = 0.; lp.lam = 0.; return lp; }
+
+    /* initial values for Newton-Raphson method */
+    lp.phi = xy.y; lp.lam = xy.x;
+    do {
+        iter = 0;
+        do {
+            sl = sin(lp.lam * 0.5); cl = cos(lp.lam * 0.5);
+            sp = sin(lp.phi); cp = cos(lp.phi);
+            D = cp * cl;
+                C = 1. - D * D;
+            D = acos(D) / pow(C, 1.5);
+                f1 = 2. * D * C * cp * sl;
+                f2 = D * C * sp;
+                f1p = 2.* (sl * cl * sp * cp / C - D * sp * sl);
+                f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;
+                f2p = sp * sp * cl / C + D * sl * sl * cp;
+                f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);
+                if (Q->mode == WINKEL_TRIPEL) {
+                f1 = 0.5 * (f1 + lp.lam * Q->cosphi1);
+                f2 = 0.5 * (f2 + lp.phi);
+                f1p *= 0.5;
+                f1l = 0.5 * (f1l + Q->cosphi1);
+                f2p = 0.5 * (f2p + 1.);
+                f2l *= 0.5;
+            }
+            f1 -= xy.x; f2 -= xy.y;
+            dl = (f2 * f1p - f1 * f2p) / (dp = f1p * f2l - f2p * f1l);
+            dp = (f1 * f2l - f2 * f1l) / dp;
+            dl = fmod(dl, M_PI); /* set to interval [-M_PI, M_PI] */
+            lp.phi -= dp;   lp.lam -= dl;
+        } while ((fabs(dp) > EPSILON || fabs(dl) > EPSILON) && (iter++ < MAXITER));
+        if (lp.phi > M_PI_2) lp.phi -= 2.*(lp.phi-M_PI_2); /* correct if symmetrical solution for Aitoff */
+        if (lp.phi < -M_PI_2) lp.phi -= 2.*(lp.phi+M_PI_2); /* correct if symmetrical solution for Aitoff */
+        if ((fabs(fabs(lp.phi) - M_PI_2) < EPSILON) && (Q->mode == AITOFF)) lp.lam = 0.; /* if pole in Aitoff, return longitude of 0 */
+
+        /* calculate x,y coordinates with solution obtained */
+        if((D = acos(cos(lp.phi) * cos(C = 0.5 * lp.lam))) != 0.0) {/* Aitoff */
+            x = 2. * D * cos(lp.phi) * sin(C) * (y = 1. / sin(D));
+            y *= D * sin(lp.phi);
+        } else
+            x = y = 0.;
+        if (Q->mode == WINKEL_TRIPEL) {
+            x = (x + lp.lam * Q->cosphi1) * 0.5;
+            y = (y + lp.phi) * 0.5;
+        }
+    /* if too far from given values of x,y, repeat with better approximation of phi,lam */
+    } while (((fabs(xy.x-x) > EPSILON) || (fabs(xy.y-y) > EPSILON)) && (round++ < MAXROUND));
+
+    if (iter == MAXITER && round == MAXROUND)
+        {
+            pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
+            /* fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl); */
+        }
+
+    return lp;
+}
+
+
+static PJ *setup(PJ *P) {
+    P->inv = s_inverse;
+    P->fwd = s_forward;
+    P->es = 0.;
+    return P;
+}
+
+
+PJ *PROJECTION(aitoff) {
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+    if (0==Q)
+        return pj_default_destructor(P, ENOMEM);
+    P->opaque = Q;
+
+    Q->mode = AITOFF;
+    return setup(P);
+}
+
+
+PJ *PROJECTION(wintri) {
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+    if (0==Q)
+        return pj_default_destructor(P, ENOMEM);
+    P->opaque = Q;
+
+    Q->mode = WINKEL_TRIPEL;
+    if (pj_param(P->ctx, P->params, "tlat_1").i) {
+        if ((Q->cosphi1 = cos(pj_param(P->ctx, P->params, "rlat_1").f)) == 0.)
+            return pj_default_destructor (P, PJD_ERR_LAT_LARGER_THAN_90);
+    }
+    else /* 50d28' or acos(2/pi) */
+        Q->cosphi1 = 0.636619772367581343;
+    return setup(P);
+}